A main contributor to cost in digital demodulators used in radio receivers is the channel filter (lpfq_rx, lpfi_rx), which is a Finite Impulse Response (FIR) filter. To achieve the necessary rejection of unwanted signals, in particular for conformance with Third Generation Partnership Project (3 GPP) specifications, a large number of filter coefficients are required. This results in an FIR filter with many coefficients (each of high bit width).
Two optimisation techniques are known to be used in digital demodulators namely subsampling on the one hand, and on the other hand IQ channel filter optimisation by combination of the filtering with quadrature down conversion.
Subsampling is a recognised technique for reduction in the number of Intermediate Frequencies (IF) used in wideband radio receivers. Subsampling is primarily used to compensate for the limitations in known Analogue-to-Digital-Converters (ADC), with respect to their maximum sampling frequency and dynamic range. The digital intermediate frequency IF is reduced to a frequency of (fsignal mod Fsample) suitable for subsequent processing.
IQ channel filters are known to be optimised so as to reduce the number of Multiply-and-ACcumulate (MAC) engines required by the filter. This is done by combination with the quadrature down conversion stage; quadrature down conversion being the process by which a digital intermediate frequency (IF) at one quarter of the sampling frequency (Fsample/4) is shifted to baseband (0 Hertz). This process involves multiplications by the following sequences:
Real part (cos θ)1, 0, −1, 0 . . .Imaginary part (sin θ)0, 1, 0, −1, . . .
By first multiplying the coefficients of the FIR filter by the above sequences, alternate coefficients become zero, thereby removing the need for every other MAC engine which would otherwise be required in the FIR filter. The computational intensity is thus halved provided the requirement is met that the digital IF is one quarter of the sampling frequency. However, as the digital intermediate frequency IF signal produced in a sub-sampling receiver is determined by the ADC sample rate and the selected analogue intermediate frequency (IF), it is not always possible to obtain a digital intermediate frequency IF at Fsample/4 so as to achieve this computational simplicity. There are often frequency spur considerations or existing architectural constraints, which prevent an analogue intermediate frequency (IF) being selected. The limitations of ADC converters are commonly recognised as one of the major design constraints in the field of radio receivers.